時窗限制下之中國郵差問題｜國立清華大學博碩士論文庫

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研究生：	溫玉彬 Yu-Pin Wen
論文名稱：	時窗限制下之中國郵差問題 Time-Constrained Chinese Postman Problems
指導教授：	王小璠 Hsiao-Fan Wang
口試委員:
學位類別：	碩士 Master
系所名稱：	工學院 - 工業工程與工程管理學系 Department of Industrial Engineering and Engineering Management
論文出版年：	2001
畢業學年度：	89
語文別：	英文
中文關鍵詞：	中國郵差問題、時窗限制、模糊集合理論
外文關鍵詞：	Chinese Postman Problem, Time Window Constraint, Fuzzy Set Theory
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中國郵差問題(Chinese Postman Problem)首先是在西元1962年由管梅谷先生所提出的，旨在探討如何在巡迴成本最低的情況下，求出一迴路使其經過所有的街道並回到點。通常為使其更符合實際情形，除了必須經過所有的街道之外，大略來說還考慮道路的有向與否。不過在現在的社會中，時間的考量也是另一個重點。在過去的文獻中，主要是以道路的方向性為探討對象，至於時間因素的限制就少有人著墨。在本論文裡，我們探討一種具有時窗限制的中國郵差問題(Time-Constrained Chinese Postman Problem)，藉由時窗的限制而能達到更多實際情形的要求。
最後引用模糊集合理論(Fuzzy Set Theory)的觀念，使得我們能夠處理時間限制的不確定性。

The Chinese Postman Problem was first proposed by the Chinese mathematician Meigu Guan (1962). It says that a postman picks up mails at the post office, delivers it along a set of streets, and returns to the post office. In practice, apart from the requirement of traveling all streets, we consider the street direction, number of postmen, and the capacity of postman etc.. But in present environment of “time is money”, the consideration is necessary. In this paper, we investigate a Chinese Postman Problem with time window constrained such that this problem can simulate the real situations.
Finally, we employ the concept of Fuzzy Set Theory to cope with a Directed DCPP when time constraints are not certain.

ABSTRACT ………………………………………………………….       Ⅰ
ACKNOWLEDGEMENT …………………………………………………       Ⅲ

CONTENTS ………………………………………………………….       Ⅳ

FIGURE CAPTIONS………………………………………………...       Ⅵ

LIST OF NOTATIONS………………………………………………        Ⅶ

CHAPTER 1  INTRODUCTION……………………………………...       1

CHAPTER 2  LITERATURE REVIEW…………………………………       3

  2.1 Notations and Definitions……………………      3

  2.2 The Chinese Postman Problem…………………      5

  2.2.1 The Undirected Chinese Postman Problem (UCPP)        5

  2.2.2 The Directed Chinese Postman Problem (DCPP) ..       9

  2.2.3 The Mixed Chinese Postman Problem (MCPP) …….       12

  2.3 Time-Constrained Traveling Salesman Problem (TCTSP)………………..................................      14

  2.3.1 Solution Procedure of TCTSP …………………… 16

  2.3.2 Applications of TCPP ……………………………….       19

  2.4 Discussion and Conclusions …………………………        19

CHAPTER 3  A MODEL FOR THE TIME-CONSTRAINED CPP……….       21

  3.1 Mathematical Model of DCPP ………………………….       21

  3.1.1 Construction of a DCPP Model …………………..        21

  3.1.2 Example for the DCPP Model ………………………        24

  3.1.3 Analysis of Variable K …………………………...       25

  3.2 Time-Constrained DCPP ……………………………….        26

  3.2.1 Construction of Time-Constrained DCPP Model ..       27

  3.2.2 Example for the Time-Constrained DCPP Model ..       28

  3.2.3 Existence of the Solution …………………………       28

CHAPTER 4  FUZZY TIME-CONSTRAINED DCPP………………….        33

  4.1 Time Constraints as Fuzzy Numbers ……………...        33

  4.1.1 Example for Model Ⅳ ……………………………..        36

  4.2 Time Constraints as Fuzzy Relations …………...        37

  4.2.1 Example for Model Ⅴ ……………………………..        39

  4.3 Discussion ………………………………………………        40

CHAPTER 5  CONCLUSIONS AND DISCUSSION…………………...       43

REFERENCES ……………………………………………………….       45

APPENDIX: TEST PROBLEMS………………………………………        47

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[6] James R. Evans and Edward Minieka, Optimization Algorithms for Network and Graphs, 2nd ed., Marcel Dekker, New York (1992).
[7] J. Edmonds and E. L. Johnson, Matching, Euler Tours and the Chinese Postman, Mathematical Programming, 5, 88-124 (1973).
[8] Abraham Kandel, Fuzzy Mathematical Techniques with Applications, Addison Wesley (1986).
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[11] L. Yaxiong and Z. Yongchand, A New Algorithm for the Directed Chinese Postman Problem, Computers and Operations Research, 1(15), 577-584(1988).

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